To multiply polynomials, we use the distributive law
[tex]\begin{gathered} (2x+1)(3x^4+7x+2)=(2x+1)(3x^4)+(2x+1)(7x)+(2x+1)(2) \\ =2x(3x^4)+1(3x^4)+2x(7x)+1(7x)+2x(2)+1(2)_{} \\ =6x^5+3x^4+14x^2+7x+4x+2 \end{gathered}[/tex]The last part follows by the laws of exponentials, finally we combine like terms
[tex]\begin{gathered} 6x^5+3x^4+14x^2+7x+4x+2=6x^5+3x^4+14x^2+(7+4)x+2 \\ =6x^5+3x^4+14x^2+11x+2 \end{gathered}[/tex]Kaylee has a bag of candy full of 15 strawberry chews and 5 cherry chews that she eatsone at a time. Which word or phrase describes the probability that she reaches inwithout looking and pulls out an orange chew?impossiblelikelySubmit Answeran equal chance or 50-50O unlikely
Given that:
- There are 15 strawberry chews in the bag.
- There are 5 cherry chews in the bag.
You know that there is no orange chew in Kaylee's bag. Therefore, knowing this, you can determine that the probability that Kaylee reaches in without looking and pulls out an orange chew is:
[tex]P=0[/tex]By definition, the probability is zero when it is impossible for the events to happen.
Since there is no orange chew in her bag, it is impossible that she reaches in
without looking and pulls out an orange chew.
Hence, the answer is: Impossible.
Write an expression to represent:The sum of one and the product of one and a number I.Stuck? Watch a video or use a hint.Written in expression to represent the sum of one and a product of one and a number x
In this case, we'll have to carry out several steps to find the solution.
Step 01:
We must analyze the problem to write the expression.
Step 02:
The expression is:
x = number
1 + 1 * x
The solution is:
1 + 1 * x
Need help with this question please!
Answer: the picture
Step-by-step explanation:
Sam and Sophia participates in a dice game. Sophia rolls one die. She gets $2 if 5 turns up. She gets $3 if 6 turns up. She loses $10 if 2 turns up. She neither wins nor loses if any other face turns up. Is this game fair?The game is not fair and not favorable to player.The game is not fair, but favorable to player.The game is fair.The game is fair, but not favorable to player.
Hello there. To solve this question, we need to analyze the probabilities for each case and see if the game is fair or not and also favorable to the player.
Sophia rolls a dice. If 5 turns up, she gets $2; If 6 turns up, she gets $3; If 2 turns up, she loses $10; She neither wins nor loses if any other face turns up.
First, let's remember something that will be important: a dice only haves 6 faces.
As we can see, she is winning (getting money) if 2 out of 6 faces turns up (5 and 6), and is losing if 1 out of 6 faces turns up (2). She is neither winning or losing if 3 out of 6 faces turns up (1, 3, 4).
About the fairness of the game, there are only 1 case she loses and 2 cases she wins something. We could only say the game is fair if the amount of winning cases were equal to the amount of losing cases. The game is not fair.
About being favorable, we'll consider it being unfavorable just the case that she loses money. The first and third cases, in which she gets money or doesn't get or lose money are favorable to her.
Since only 1 out of 6 faces makes her lose, then the game is favorable to the player.
Final answer: The game is not fair, but favorable to the player.
8Σ-(-2): -1-i=1Evaluate each geometric series described. (Find the total sum)
The given expression is
[tex]\sum ^8_{i\mathop=1}-(-2)^{i-1}[/tex]To solve this, we just have to replace each value of the sum in the expression, then we sum. Let's do it
[tex]\begin{gathered} -(-2)^{1-1}=-1 \\ -(-2)^{2-1}=-(-2)^1=2 \\ -(-2)^{3-1}=-(-2)^2=-4 \\ -(-2)^{4-1}=-(-2)^3=8 \\ -(-2)^{5-1}=-(-2)^4=-16 \\ -(-2)^{6-1}=-(-2)^5=-(-32)=32 \\ -(-2)^{7-1}=-(-2)^6=-64 \\ -(-2)^{8-1}=-(-2)^7=-(-128)=128 \end{gathered}[/tex]Now, we sum all these items
[tex]-1+2-4+8-16+32-64+128=85[/tex]Therefore, the total sum is 85.Help solving these problems
Therefore, when daily output is 106300 units, the cost will be at its lowest.
Define costs.The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function. The average cost function is defined as A(x)=C(x)x, where x > 0. The average cost per unit is calculated by dividing the total cost by the number of units produced. Costing is necessary to make sure that all costs are met and that the group decides on a price that will result in a profit. Finding ALL of a company's costs, including manufacturing, sales, administration, overhead, etc., is the first and most crucial stage. Costs are then divided into fixed and variable costs.
Given,
C=0.04x2 - 8.504x + 25302....... (1), where x is the number of units produced in thousands, gives the cost of generating x thousands of units of lemon-scented widgets in a day.
We must determine the daily production rate that will reduce costs.
dC/dx = 0
The current prerequisite for minimum cost is
0.08x - 8.504 = 0
0.08x = 8.504
x = 106.3
In light of equation (1),
x =106.3
Therefore, when daily output is 106300 units, the cost will be at its lowest.
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Two observation posts A and B are 12 km apart. A third observation post C is located 15 km from A such that CBA is 67º. Find the measure of CÂB
Using the law of sines:
[tex]\begin{gathered} \frac{AB}{\sin(C)}=\frac{AC}{\sin (B)} \\ so\colon \\ \sin (C)=\frac{AB\cdot\sin (B)}{AC} \\ \sin (C)=\frac{12\cdot\sin (67)}{15} \\ C=\sin ^{-1}(\frac{12\cdot\sin(67)}{15}) \\ C\approx47.43^{\circ} \end{gathered}[/tex]Using the triangle sum theorem:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ so\colon \\ x+47.43+67=180 \\ x=180-67-47.43 \\ x=m\angle C=m\angle CAB=65.57^{\circ} \end{gathered}[/tex]Which describes a bar diagram showing the percent of students who participated in dances?1 shaded square out of 10 squares2 shaded squares out of 10 squares3 shaded squares out of 10 squares4 shaded squares out of 10 squares
From the information on the pie chart, the proportion of students that participated in dances is 20 out of 100.
Then, if we represent this in a bar chart where 100% is 10 squares, the proportion of students that participated in dances should be represented by:
[tex]\begin{gathered} 100\%\longrightarrow10\text{ squares} \\ \frac{20}{100}\cdot100\%=20\%\longrightarrow\frac{20\%}{100\%}\cdot10=2\text{ squares} \end{gathered}[/tex]Answer: 2 shaded squares out of 10 squares
A firm uses trend projection and seasonal factors to simulate sales for a given time period.
It assigns "0" if sales fall, "1" if sales are steady, "2" if sales rise moderately, and "3" if sales
rise a lot. The simulator generates the following output.
0102200123202022123122203002121
Estimate the probability that sales will rise at least moderately.
Answer:
3
Step-by-step explanation:
0+1=1-1+0+2=3-3+1+2+0-1=4
Telephone numbers are in the form NYZ-ABC-XXXX. the following restrictions were placed; N can only be numbers: 2-9; Y can only be numbers 0-7 and A&C cannot be 2. how many phone numbers are there?
Answer
The answer = 5,184,000,000
There are 5,184,000,000 possible phone numbers.
Explanation
The question told us that telephone numbers are in the form NYZ-ABC-XXXX, then proceeds to give us the restrictions on some of the positions available.
- N can only be numbers: 2-9;
- Y can only be numbers 0-7
- and A&C cannot be 2
We are then told to calculate the number of phone numbers possible.
This question is a special type of permutation and combination.
To solve it, it will be a multiplication of the possible numbers that can take up each position.
N, can only be numbers 2 to 9. Number of possible digits = 8
Y, can only be numbers 0 to 7. Number of possible digits = 8
Z, no restriction, can have numbers 0 to 9. Number of possible digits = 10
A, number cannot be 2. Number of possible digits = 9
B, no restriction, can have numbers 0 to 9. Number of possible digits = 10
C, number cannot be 2. Number of possible digits = 9
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
Total number of possible phone numbers
= 8 × 8 × 10 × 9 × 10 × 9 × 10 × 10 × 10 × 10
= 5,184,000,000
Hope this Helps!!!
____+3/10=3/15 option 3/5
First we can simplify the result
[tex]\frac{3}{15}=\frac{1}{5}[/tex]in order to know the missing fraction, we will call x
[tex]\begin{gathered} x=\frac{1}{5}-\frac{3}{10} \\ x=-\frac{1}{10} \end{gathered}[/tex]we can check it
[tex]-\frac{1}{10}+\frac{3}{10}=\frac{2}{10}=\frac{1}{5}=\frac{3}{15}[/tex]A printer prints 5 photos each minute. Let P be the number of photos printed in M minutes. Write an equation relating P to M. Then graph your equation using the axes below.
The equation is:
P = 5M
The graph is shown in the explanation
Explanation:Given that a printer prints 5 photos per minute.
Since P represents the number of photos printed in M minutes, we have:
[tex]P=5M[/tex]The graph of this is shown below:
01018Annual SalaryANNUAL SALARY VERSUSYEARS OF SERVICE$60,000$50,000$40,000$30,000$20,0005 10 15 20Years of ServiceIn the scatterplot above, each dot represents the annual salary and corresponding years of service for each ofthe 19 employees at Company X. How many of the employees have more than 10 years of service but anannual salary of less than $40,000 ?
To determine how many employees have more than 10 years of service we need to look for dots that are to the right of the "10" position on the horizontal axis. There are a total of 11 employees that fit that criterion. We now need to look for which of these 11 employees earn less than 40,000 per year, for that we have to find the number of dots below the line of 40,000 and to the right of 10 years of service. There are a total of 5 dots.
There are 5 employees with more than 10 years of service which earn less than $40,000.
Enter the digit that can replace (blank box) 526 < 5 _ 5 < 541 The digit that fits in the gray box is ?
3
1) The number to be found, is a multiple of 5 and also greater than 526 but also lesser than 541.
2) So we have, the next number whose last digit is 5 immediately greater than 526 and lesser than 541 is 535
3) So 3 is the missing digit
One-sixth of the fourth graders and one-third of the fifth graders miss school on Friday. The absentee sheet for Friday shows the names of 9 fourth graders and 16 fifth graders. How many fourth and fifth graders are enrolled in the school?
Answer:
There are 54 4th graders.
There are 48 5th graders.
Step-by-step explanation:
1/6 of the 4th graders is 9 students.
1/6 x = 9
x = 9 × 6
x = 54
There are 54 4th graders.
1/3 of the 5th graders is 16 students.
1/3 x = 16
x = 3 × 16
x = 48
There are 48 5th graders.
There are 54 Fourth grader and 48 Fifth graders were enrolled in the school.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number of fourth graders be x.
and, let the number of fifth graders be y.
As, One-sixth of the fourth graders is 9.
and, one-third of the fifth graders is 16.
Then, 1/6 x = 9
x= 54
and, 1/3 y= 16
y= 48
Hence, there are 54 Fourth grader and 48 Fifth graders were enrolled in the school.
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- Consider the function represented by this table of values.Xу6385324263 202 14Which function could have produced the values in the table?Ay = 6x + 2By = -6x + 2C) y = (x - 116y = -x - 44
Upload the picture please,
First you need to find the slope using the formula
Slope = (y2 - y1) / (x2 - x1)
Choose two points from the table
P1 = (6, 38)
P2 = (5, 32)
Identify x1, y1, x2, y2
x1 = 6 y1 = 38 x2 = 5 y2 = 32
Substitute the values to find the slope
slope = m = (32 - 38) / (5 - 6)
= -6/-1
= 6
Find the equation of the line using the formula
y - y1 = m(x - x1)
x1 = 6 y1 = 38
Substitution
y - 38 = 6(x - 6)
Simplify
y - 38 = 6x - 36
Solve for y
y = 6x - 36 + 38
y = 6x + 2
6. The budget for a new house can only afford 1/4 of the floor area to be done inceramic tile. The rest of the floor area will be carpeted. The size of the kitchen areahas not yet been determined. Not including the kitchen, the architect has alreadydesigned 2200 square feet of floor area, 15% of which has tile floors specified.What area, in square feet, can be planned for the kitchen if its entire floor area is tohave ceramic tile? Assume all values are ex
The budget of a new house can only afford 1/4 of the floor area
the total area of the floor is designed to be 2200 square feet
15% of the floor is tiled
let the budget be x
area to be done in ceramic tile is 1/4 x the total budget
1/4 * 2200 = 550
550 square feet area of the floor will be use for ceramic tiles alone
helpppppppppppppppppppp
Ben needs to graph the function f(x)=3(0.1)x. He creates a table of values, using integer values for x.
What does Ben's graph look like?
Drag a value or word to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
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Ben's graph passes through the ordered pairs (−1,Response area), (0, Response area), and (2,Response area). The graph Response area left to right.
Answer:
is there a pitcher that comes with it ?
Step-by-step explanation:
5x + 12 - 9x - 4 - 16
This problem is about a simple algebraic expression which we need to reduce in its simplest form. To do that, we need to reduce like terms, that is, terms that are similar, for example, terms 5x and 9x are similar because they have the same variable; also terms 12, 4, and 16 are also similar because they are single numbers.
Now, we reduce them using the algebraic sum properties, that is, numbers with the same sign will sum, and numbers with different signs will subtract:-
[tex]5x+12-9x-4-16[/tex]Then, we have
[tex]-4x-8[/tex]Therefore, the simplest expression is -4x-8.Long divide 4x^4-3x^3+1 / x-5
We have the following division:
for this, we have to divide each remainder by x, and use the law of signs in reverse order. The division will look like this:
Therefore, the result of the division is:
[tex]\frac{4x^4-3x+1}{x-5}=4x^3+17x^2+85x+425+\frac{2126}{x-5}[/tex]Maria invested her savings in two investment funds. The amount she invested in Fund A was $7000 less than the amount she invested in Fund B. Fund Areturned a 7% profit and Fund B returned a 3% profit. How much did she invest in Fund B, if the total profit from the two funds together was $1610?
It is given that,
The amount she invested in Fund A was $7000 less than the amount she invested in Fund B.
So, A=B-7000
And it is given that, Fund A returned a 7% profit and Fund B returned a 3% profit.
The total profit from the two funds together was $1610.
It can be written as,
7% of A +3% of B=1610
Substitute A=B-7000, we get
7% of (B-7000) +3% of B=1610
On solving we get,
[tex]\begin{gathered} \frac{7}{100}(B-7000)+\frac{3}{100}B=1610 \\ \frac{7}{100}B-490+\frac{3}{100}B=1610 \\ \frac{10}{100}B-490=1610 \\ \frac{1}{10}B=1610+490 \\ \frac{1}{10}B=2100 \\ B=21000 \end{gathered}[/tex]Hence, the investment in fund B is $21,000.
Transform 12 + 3y = 9 into an equivalent equation that is in slope-intercept form.A. y=3/4x - 1/4B. y=-4x+3C. y=4x-3D. y=-1/4x+3/4
Given:
[tex]12x+3y=9[/tex]Find: Slope - intercept form.
Sol:
Slope - intercept form:
[tex]y=mx+c[/tex][tex]\begin{gathered} 12x+3y=9 \\ 3y=-12x+9 \\ y=\frac{-12}{3}x+\frac{9}{3} \\ y=-4x+3 \end{gathered}[/tex]Slope intercept form of equation is:
[tex]y=-4x+3[/tex]Kimberly and Clay leaves a concert hall at the same time, traveling in buses going opposite directions, Kimberly's bus tra els at 40mph and Clay's bus travels at 60mph. In how many hours will Kimberly and Clay be 350 miles apart?
let s1 and s2 be the distance covered by the two buses
s1 + s2 = 350 ................................eqn I
velocity (v) = distance (s)/time (t) .........................eqn II
from eqn II the velocity of the first bus, v1 = s1/t1
s1 = v1t1 .................................eqn III
velocity of the second bus, v2 = s2/t2
s2 = v2t2 ...........................eqn IV
substitute eqn III and eqn IV into eqn I
v1t1 + v2t2 = 350
the time taken for any two moving objects to simultaneously cover any distance is equal. Thus,
t1 = t2 = t
eqn V becomes
v1t + v2t = 350
t(v1 + v2) = 350
v1 = 40
v2 = 60
t(40 + 60) = 350
100t = 350
divide both sides by 100
100t/100 = 350/100
t = 3.5 hours
Ty hiked up a mountain to 2523 meters above sea level. Pete is a scuba diver and dove 319 meters below sea level. If Ty and Pete started at the same elevation, how much higher was Ty than Pete when they were the farthest apart?
Ty hiked up a mountain to 2523 meters above sea level.
Height of the TY above the sea level = 2523meter
. Pete is a scuba diver and dove 319 meters below sea level
Depth of the Pete = 319 meter
To find the how much higher was Ty than Pete,
Find the differecne between thier disatnce from sea level
[tex]\begin{gathered} Ty\text{ was higher than Pete=2523-319} \\ Ty\text{ was higher than pete by }2204\text{ meter} \end{gathered}[/tex]Answer: Ty was 2204 meter higher than Pete
A ball is dropped from a height of 18 feet.The function f(x) = 18(0.75)* gives theheight in feet of each bounce, where x isthe bounce number. What will be theheight of the third bounce to the nearesttenth of a foot?
The height of the third bounce to the nearest tenth of a foot is 7.6 ft
Explanation:The given function:
[tex]f(x)\text{ = }18\mleft(0.75\mright)^x[/tex]f(x) = height in feet of each bounce
x represent the bounce number
For the third bounce, x = 3
replacing x with 3:
[tex]\begin{gathered} f(x)=18(0.75)^3 \\ f(x)\text{ = 18(0.4219)} \end{gathered}[/tex][tex]\begin{gathered} f(x)\text{ = }7.5942 \\ To\text{ the nearest tenth of foot = 7.6 ft} \end{gathered}[/tex]The height of the third bounce to the nearest tenth of a foot is 7.6 ft
5) Solve for x:X - 7.5 = 186) Solve for x:45x = 14.5
We have the following:
5)
[tex]x-7.5=18[/tex]solving for x:
[tex]\begin{gathered} \text{let's add 7.5 on each side} \\ x-7.5+7.5=18+7.5 \\ x=25.5 \end{gathered}[/tex]6)
[tex]\begin{gathered} 45x=14.5 \\ \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} \text{ divide on each side by 45} \\ x=\frac{14.5}{45} \\ x=0.32 \end{gathered}[/tex]Original price of a camera: $799.95Discount: 17%What's the selling price
Answer:
$663.95
Explanation:
Given the following:
Original price of a camera: $799.95
Discount: 17%
Discounted price = 17% of original price of the camera
Discounted price = 0.17*$799.95
Discounted price = $135.99
Selling price = Original Price - Discounted price
Selling Price = $799.95 - $135.99
Selling price = $663.96
Hence the selling price is $663.95
can you please solve this practice problem for me I need assistance C. -1/2 and D. 1/2
We are going to select the points when x = 0 and x = 2.
Observing the graph we see that when x = 0, then y = 1 - (0,1)
when x = 2, then y = 2 - (2, 2)
Now we have two points:
(x₁, y₁) = (0, 1)
(x₂, y₂) = (2, 2)
Step 2: change of variablesWe are going to find how much the variables change from point 1 to point 2
Change of x:
Δx = x₂ - x₁ = 2 - 0 = 2
Δx = 2
Change of y:
Δy = y₂ - y₁ = 2 - 1 = 1
Δy = 1
Step 3: slopeThe slope, m, is the division of the two found changes:
m = Δy/Δx = 1/2
Answer: D. 1/2If g(x) = 2x-10 what is g(7)?
Answer:
4
Explanation:
Given the below function;
[tex]g(x)=2x-10[/tex]To find g(7), all we need to do is substitute the x for 7 in the below and solve;
[tex]g(7)=2(7)-10=14-10=4[/tex]What Values of x make two expressions below equal?(X+3)(x+8) = x+3————— —— 5(x+8) 5
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
( OPTION C )